The Tianjin explosion and the scaling laws of nuclear weapons


Senior Member.
Some commentators have claimed the Tianjin explosion was caused by a tactical nuke. However this does not fit with the known scaling laws of the effects of nuclear weapons. They seem to think a small nuke is exactly like a big nuke, only smaller and cuter.

Glasstone and Dolan (1977) wrote the definitive work on the effects of nuclear weapons and I cite their work throughout.

The blast radius increases with the cube root of the yield. The prompt ionizing radiation radius increases to the 0.19 power of the yield. The radius of the fireball of a surface burst increases to the 0.4 power of the yield. The time after detonation of the peak of the thermal radiation output increases to the 0.44 power of the yield. And the duration of the fireball is 10 times the time of the peak thermal output. That means if you time the duration of the fireball you can calculate the yield. This compilation video of the explosion includes a security cam with a timestamp.

The fireball lasts for 22 seconds so the peak thermal power occurred at 2.2 seconds after detonation. Plug in the numbers for the time of peak thermal radiation output and it comes up with a yield of 8.2 megatons!!!

Another way to estimate yield is to measure the radius of the fireball. thunderf00t did that in this video and came up with a radius of 75 meters:

Section 2.127 describes the scaling and constants of the radius of the fireball:

For a surface burst that radius would indicate a yield of 0.66 kilotons. But that yield would give a fireball duration of 0.34 seconds.

Since two extremely well-studied phenomena of nuclear weapons give incredibly huge discrepancies in yield (8200 and 0.66 kilotons), and the observed fireball radius and fireball duration are mutually exclusive, it is very safe to say this explosion came no where near to obeying the scaling laws of nuclear weapons and therefore it was not caused by a nuclear weapon.
Comparing the damage of the Tianjin blast to some other powerful explosions shows similar effects.

First up the Flixborough disaster of 1974

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A major leak of liquid from the reactor circuit caused the rapid formation of a large cloud of flammable hydrocarbon. When this met an ignition source (probably a furnace at a nearby hydrogen production plant) there was a massive fuel-air explosion. The plant control room collapsed, killing all 18 occupants. Nine other site workers were killed, and a delivery driver died of a heart attack in his cab. Fires were started on-site which were still burning 10 days later. Around 1,000 buildings within a mile radius of the site (in Flixborough itself, and in the neighbouring villages of Burton upon Stather and Amcotts) were damaged, as were nearly 800 in Scunthorpe (three miles away); the blast was heard over thirty miles away in Grimsby and Hull.
and there are reports of some parts of the plant being found 12 miles away.
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As the shock wave tore across the Humber, the two-man crew of a Hull barge were hurled across their vessel by the force of the blast. Arthur Hall, of Newcomen Street, Southcoates Lane, and Mr Ronald Bentley, of Waveney Road, Longhill Estate, escaped with bruises.

In North Ferriby, a 10ft long piece of corrugated iron sheeting fell from the sky. It had travelled about 12 miles from the chemical plant.

Second up the Soham explosion from 1944
Although a lot smaller than the above blast, it was a railway wagon loaded with bombs, it still created a large crater and had a devastating blast.
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The explosion created a crater 66 feet (20.1 m) in diameter and 15 feet (4.6 m) deep, the station buildings were almost demolished and there was damage severe or moderate to over 700 properties within 900 yards (823 m).
and finally something far more recent... the Buncefield fire and explosion

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Because of an inversion layer, the explosions were heard up to 125 miles (200 km) away; there were reports that they were audible in Belgium, France, and the Netherlands.

The British Geological Survey monitored the event, which measured 2.4 on the Richter scale. It was reported that people were woken in south London, and as far west as Wokingham (about 28 miles (45 km)), where in its southern suburb, Finchampstead, numerous people felt the shockwave after the initial explosion. Subsequent explosions occurred at 06:27 and 06:28.

Witnesses many miles from the terminal observed flames hundreds of feet high; the smoke cloud was visible from space, and from as far north as Lincolnshire (about 70 miles (110 km)) away. Damage from the blasts included broken windows at various buildings including the Holy Trinity church and Leverstock Green School, blown-in or warped front doors, and an entire wall being removed from a warehouse more than half a mile (800 m) from the site.[17] Buildings in neighbouring St Albans also suffered; Townsend School had serious blast damage, and a window was blown out of St Albans Abbey (about 5 miles (8 km)).

Several nearby office blocks were hit so badly that almost every window, front and back, was blown in as the explosion ripped through them. During the working day, these offices would have been full of people, and many deaths may have resulted. Reports also indicated that cars in nearby streets caught fire. The roof of at least one house was blown off. Buildings in the vicinity were evacuated by police, not only because of the smoke and possibility of more explosions, but because of the danger of structural damage making the buildings unstable.
I live 110 miles from Buncefield and I heard it!!

Have a read of the reports, the effects of all three blasts (and these are just the three that sprang to mind, there are many others) do not differ in effect and result from the Tianjin blast (apart from variations in scale)

Bottom line is you don't need a nuke to make a large and very devastating bang, petrol chemicals and hydro-carbons are more than capable of doing that all by themselves give enough of them and an ignition source.
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They seem to think a small nuke is exactly like a big nuke, only smaller and cuter.

This is not the first time the ill-informed have claimed any large explosion is a 'tactical nuke', 'mini nuke' or even 'neutron bomb' on the basis of a fireball and mushroom cloud:

What they fail to notice is the lack of blinding flash, the cameraman remaining alive to film the scene and the total and utter lack of any increased radiological activity of any sort.

But it must be true, because they saw it on the internet....
They only believe what they see with their own eyes, and most importantly: that is what they WANT it to be.
I linked to it previously but it got lost in the shuffle:

So the quote is in 7.86:

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It is seen that the time equal to 10 tmax about 80 percent of the thermal energy will have been emitted; hence time may be taken as a rough measure of the effective duration of the thermal pulse for an air burst
Where did you the idea you can use the fireball duration to estimate tmax? Is it in the book?

Have you tried using this method on known nuke videos of known yield?